While I agree with the point that "looking stupid" shouldn't matter here and that love does require risk, I don't agree with sending the letter..I actually did something similar when I was 16, and it didn't work at all, and I felt like a complete ..ever since that, I've hardened a lot in my relationships with females..
Luckily, I learned this at a young age..that failed relationship got me arrested and facing charges..I even became friends with her a few years later, but I learned to give up and accept when the relationship is over..I have learned the signs and when to get out..a lot of these girls turn out to be gaping, even though we're scared to look at the depth of the hole, past the puddles..
Another important point is that even if you guys do get back together, there's a good chance that things will never be the same..you'll always wonder why she left you, and she probably won't want to talk about it, which in itself, will cause fights..you'll always wonder whether another guy was involved..it'll never leave your head IMO, even if you think it might..you would have to be a really, really mature man to forget it..
Sometimes, you really just have to accept that something is over, it's essential..